Amyloid Fibril Seeded Polymerization Kinetics

k_n (primary) 1e-4 k_+ (elongation) 1e0 k_2 (secondary) 1e-3 k_off (depolymer.) 1e-2 n_c (nucleus size) 3 n_2 (2° nuc size) 2

m_0 (monomer) 5 μM Seed fraction 0%

t_half (s)—

Final fibril %—

Max rate—

Regime—

Elongation: dP/dt = k_n m^{nc} + k_2 M m^{n2}

Mass: dM/dt = 2k_+ m P − 2k_off P

Monomer: dm/dt = −dM/dt − nc·(nucl.)

Knowles 2009 (PNAS): exact solution for linear regime

Seeding: add initial P_0, M_0 → eliminates lag phase

M = fibril mass concentration
P = number of fibril ends

Amyloid Fibril Polymerization Kinetics